Explicit controller formulas for LMI-based H∞ synthesis

Automatica

Volumn 32, Issue 7, 1996, Pages 1007-1014

  Gahinet, Pascal ^a  

^a MATHWORKS INC   (United States)

Author keywords

Continuous and discrete time systems; H control; LMI optimization; LMI based synthesis

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; CONTROL SYSTEM SYNTHESIS; CONVERGENCE OF NUMERICAL METHODS; DISCRETE TIME CONTROL SYSTEMS; LINEAR CONTROL SYSTEMS; LYAPUNOV METHODS; MATRIX ALGEBRA; OPTIMIZATION; RICCATI EQUATIONS;

CONTINUOUS TIME SYSTEMS; LINEAR MATRIX INEQUALITIES;

OPTIMAL CONTROL SYSTEMS;

EID: 0030192253     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/0005-1098(96)00033-7     Document Type: Article

References (34)

1. Anderson, B. D. O., and S. Vongpanitlerd (1973). Network Analysis. Prentice-Hall, Englewood Cliffs, NJ.
2. ∞ controllers. IEEE Trans. Autom. Control, AC-40, 853-864 (see also p. 1681).
3. ∞ control of linear parameter-varying systems. Automatica, 31, 1251-1261.
4. Boyd, S. P. and L. El Ghaoui (1993). Method of centers for minimizing generalized eigenvalues. Lin. Alg. Applic., 188, 63-111.
5. Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan (1994). Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia.
6. ∞ design with pole placement constraints: an LMI approach. IEEE Trans. Autom. Control. AC-41, 358-367.
7. David, J. and B. De Moor (1993). The opposite of analytic centering for solving minimum rank problems in control and identification. In Proc. 32nd IEEE Conf. on Decision and Control, San Antonio, TX.
8. ∞ control problems. IEEE Trans. Autom. Control, AC-34, 831-847.
9. El Ghaoui, L. and P. Gahinet (1993). Rank-minimization under LMI constraints: a framework for output feedback problems. In Proc. European Control Conf., pp. 1176-1179.
10. Fan, M. K. H. (1993). A second-order interior point method for solving linear matrix inequality problems. Submitted to SIAM J. Control Optim.
11. ∞ Control Theory. Lecture Notes in Control and Information Sciences, Vol. 88, Springer-Verlag, Berlin.
12. ∞ suboptimal controllers. In Proc. 31st IEEE Conf. on Decision and Control, Tucson, AZ, pp. 937-942.
13. ∞ control. Int. J. Robust Nonlinear Control, 4, 421-448.
14. ∞ synthesis via LMIs. In Proc. American Control Conf., Baltimore, MD, pp. 1499-1500.
15. ∞ control. To appear in SIAM J. Control Optim. Also in Proc. 33rd IEEE Conf. on Decision and Control, Lake Buena Vista, FL, 1994, pp. 1527-1532.
16. ∞ control. To appear in SIAM J. Control Optim. Also in Proc. 33rd IEEE Conf. on Decision and Control, Lake Buena Vista, FL, 1994, pp. 1527-1532.
17. Gahinet, P., A. Nemirovski, A. J. Laub and M. Chilali (1995). LMI Control Toolbox. The MathWorks Inc. Also in Proc. 33rd IEEE Conf. on Decision and Control, Lake Buena Vista, FL, 1994, pp. 2038-2041.
18. ∞-norm bound and relations to risk sensitivity. Syst. Control Lett., 11, 167-172.
19. Grigoriadis, K. M. and R. E. Skelton (1994). Fixed-order control design for LMI control design problem using alternating projection methods. In Proc. 33rd IEEE Conf. on Decision and Control, Lake Buena Vista, FL, pp. 2003-2008.
20. ∞ control problem: LMI existence conditions and state-space formulas. Automatica, 30, 1307-1317.
21. ∞ control. In Proc. 28th IEEE Conf. on Decision and Control, Tampa, FL.
22. Nemirovski, A. and P. Gahinet (1994). The projective method for solving linear matrix inequalities. To appear in Math. Programming, Ser. B, 1996. Also in Proc. 1994 American Control Conf., Baltimore, MD, pp. 840-844.
23. Nemirovski, A. and P. Gahinet (1994). The projective method for solving linear matrix inequalities. To appear in Math. Programming, Ser. B, 1996. Also in Proc. 1994 American Control Conf., Baltimore, MD, pp. 840-844.
24. Nesterov, Yu. and A. Nemirovski (1994). Interior Point Polynomial Methods in Convex Programming: Theory and Applications. SIAM, Philadelphia.
25. Packard, A. (1994). Gain scheduling via linear fractional transformations. Syst. Control Lett., 22, 79-92.
26. Packard, A., K. Zhou, P. Pandey and G. Becker (1991). A collection of robust control problems leading to LMI's. In Proc. 30th IEEE Conf. on Decision and Control, Brighton, U.K., pp. 1245-1250.
27. ∞ control problem. Int. J. Robust Nonlinear. Control, 1, 171-185.
28. ∞ theory via loop-shifting, matrix-pencil and descriptor concepts. Int. J. Control, 50, 2467-2488.
29. ∞-optimal control. PhD Thesis, University of Würzburg.
30. ∞ optimization without assumptions on finite or infinite zeros. SIAM J. Control Optim. 30, 143-166.
31. ∞ control problem with measurement feedback. SIAM J. Control Optim. 30, 182-202.
32. ∞ control problem with measurement feedback. Int. J. Robust Nonlin. Control, 4, 457-479.
33. Vandenberghe, L. and S. Boyd (1995). Primal-dual potential reduction method for problems involving matrix inequalities, Math. Programming, Ser. B, 69, 205-236.
34. 2 norm control for LPV systems with bounded parameter variation rates. In Proc. American Control Conf., Seattle, WA.